The equation is an approximation to the wheel path - it ignores factors such as rake and the natural tilt that a bicycle takes when turning.
A reasonable model of a bicycle path is to consider the following:
- The rear wheel is mounted on a rigid frame oriented in the direction the rear wheel is moving.
- The front wheel is mounted at distance L forwards of the rear wheel, on the same rigid frame, but can pivot on a vertical axis.
As a result, the rear wheel is always pointing directly at the front wheel, so you can consider that at any time $t$, if the rear wheel is at a point $R(t)$, then the the front wheel is at a point distance $L$ along a line tangent to $R(t)$.
Maybe the picture below will help.
